Question

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⏺ State the kepler's law of planetary motion. Obatain Newton's law of gravitation from the Kepler's laws. ​

Answer 1

Answer:

Kepler's laws:

1) Law of orbit :

Each planet moves around the sun in an elliptical orbit with sun at one of the foci .

2) Law of areas :

The line joining the sun and a planet sweeps out equal areas in equal intervals of time. In other words, areal velocity of a planet is constant at dA/dt = constant. The law of areas is identical with the law of conservation of angular momentum.

3) Law of periods :

The square of the time for a planet to complete a revolution about the sun is proportional to the cube of semi-major axis of the elliptical orbit.

${T}^{2} \: \alpha \: {a}^{3}$

Answer 2

Answer:

Newton's Law of Gravitation can be easily obtained from Kepler's Laws of Planetary Motion. Suppose a planet of mass m is revolving around the sun of mass M in a nearly circular orbit of radius r, with a constant angular velocity ω. Let, T be the time period of revolution of the planet around the sun.